A baton twirler releases a baton at a height of 5 feet above the ground with the initial velocity of 30 feet per second. The height of the baton t seconds after it is thrown is given by the function, ℎ(t) = −16t^2 +30t +5, where ℎ(t)is the height of the baton in feet. a.) How high is the baton after 1.5 seconds? Round your answer to the nearest hundredth, if applicable.
b.) What is the maximum height of the baton? Round your answer to the nearest hundredth, if applicable.
c.) How long does it take for the baton to reach its maximum height? Round your answer to the nearest hundredth, if applicable.
d.) She catches the baton at a height of 6 feet. How long is the baton in the air? Round your answer to the nearest hundredth, if applicable. Justify your answer.